Goal:
  
  G : t
  HI : invariants G
  HG : acyclic_no_loop G
  y_0 : V.t
  x_0 : V.t
  K : Z
  Hxs : lsp G x_0 y_0 = Some K
  s0 : VSet.t
  s' : VSet.t
  y : V.t
  z : V.t
  d : DisjointAdd y_0 s0 s'
  e : EdgeOf G' y_0 y
  q : SPath G' s0 y z
  IHq : match from_G' q with
        | inl q' => sweight q = sweight q'
        | inr (q1, q2) => sweight q <= sweight q1 - K + sweight q2
        end
  XX : (y_0, - K, x_0) = (y_0, e.π1, y)
  H0 : - K = e.π1
  H1 : x_0 = y
  ============================
   (e.π1 + sweight q <=
    - K +
    sweight
      (SPath_sub G (DisjointAdd_Subset d)
         (sum_rect
            (fun _ : SPath G s0 y z + (SPath G s0 y y_0 × SPath G s0 x_0 z)
             => SPath G s0 x_0 z)
            (fun IHq : SPath G s0 y z =>
             eq_rect_r
               (fun _pattern_value_ : V.t => SPath G s0 _pattern_value_ z)
               IHq (snd_eq XX))
            (fun IHq : SPath G s0 y y_0 × SPath G s0 x_0 z => IHq.2)
            (from_G' q))))


DEBUG:Going to execute:
<coq-core.plugins.ssreflect::ssrrewrite@0> $1 $2
DEBUG LTAC Evaluated term: (fst_eq (fst_eq XX))